Global solution to the Penrose-Fife phase-field model with zero interfacial energy and Fourier law

In this paper we study a system of field equations of Penrose-Fife type governing the dynamics of phase transitions with a nonconserved order parameter. In many recent contributions on this subject, the heat flux law has been assumed in the form q=#nabla#(1/#theta#). In contrast to that, here we consider the (more realistic) case of the Fourier law when q is proportional to the negative gradient - #nabla##theta# of the (absolute) temperature #theta#. The assumption of Fourier heat conduction presents particular difficulties in the framework of the Penrose-Fife model, since then the field equation representing the balance of internal energy does not seem to have a maximum principle from which the positivity of #theta# could be derived. In this connection, we recall that the main difficulty in proving existence for phase-field systems of Penrose-Fife type is the proof of the positivity of #theta#. It is shown in this paper that in the case without interfacial energy, that is, when the free energy does not contain a quadratic gradient term of the order parameter, there exists a comparatively easy way to conclude the positivity of #theta# under rather weak and quite natural conditions on the data of the system. Having established this result, the existence of a weak solution is readily obtained using known results on general phase-field systems. (orig.)SIGLEAvailable from TIB Hannover: RR 5549(351)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman